# American Institute of Mathematical Sciences

April  2010, 6(2): 363-380. doi: 10.3934/jimo.2010.6.363

## Smoothing Newton algorithm based on a regularized one-parametric class of smoothing functions for generalized complementarity problems over symmetric cones

 1 Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, China

Received  April 2009 Revised  December 2009 Published  March 2010

Based on the KK smoothing function, we introduce a regularized one-parametric class of smoothing functions and show that it is coercive under suitable assumptions. By making use of the introduced regularized one-parametric class of smoothing functions, we investigate a smoothing Newton algorithm for solving the generalized complementarity problems over symmetric cones (GSCCP), where a nonmonotone line search scheme is used. We show that the algorithm is globally and locally superlinearly convergent under suitable assumptions. The theory of Euclidean Jordan algebras is a basic tool in our analysis.
Citation: Xiao-Hong Liu, Wei-Zhe Gu. Smoothing Newton algorithm based on a regularized one-parametric class of smoothing functions for generalized complementarity problems over symmetric cones. Journal of Industrial & Management Optimization, 2010, 6 (2) : 363-380. doi: 10.3934/jimo.2010.6.363
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